MATHEMATICAL MODELING OF FISH POPULATION GROWTH WITH HARVESTING

Abstract

In this research work, we proposed and analyzed a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones: a free fishing zone and a reserve zone where fishing is strictly prohibited. Biological and bionomic equilibria of the system are obtained, and the existence of possible steady states, along with their local and global stability, is discussed. It is shown that even if fishery is exploited continuously in the unreserved zone, fish populations can be maintained at an appropriate equilibrium level in the habitat. We then examine the possibilities of the existence of bionomic equilibrium. An optimal harvesting policy is also discussed using the Pantryagin’s Maximum Principle. Numerical simulations with MATLAB have been performed to study the effects of various parameters on the dynamics of the population biomass.